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    Authors: Kmit, I.

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    Relation: mr:MR2863995; zbl:Zbl 1247.47044; reference:[1] Adams R.A.: Sobolev spaces.Academic Press, New York, 1975. MR 0450957; reference:[2] Akramov T.A.: On the behavior of solutions to a certain hyperbolic problem.Siberian Math. J. 39 (1998), no. 1, 1–17. Zbl 0934.35013, MR 1623699, 10.1007/BF02732355; reference:[3] Akramov T.A., Belonosov V.S., Zelenyak T.I., Lavrent'ev M.M., Jr., Slin'ko M.G., Sheplev V.S.: Mathematical Foundations of Modeling of Catalytic Processes: A Review.Theoretical Foundations of Chemical Engineering 34 (2000), no. 3, 295–306. 10.1007/BF02755974; reference:[4] Appell J., Zabrejko P.: Nonlinear Superposition Operators.Cambridge University Press, Cambridge, UK, 1990. Zbl 1156.47052, MR 1066204; reference:[5] Chow S.-N., Hale J.K.: Methods of Bifurcation Theory.Grundlehren der Math. Wissenschaften, 251, Springer, New York-Berlin, 1982. Zbl 0487.47039, MR 0660633, 10.1007/978-1-4613-8159-4; reference:[6] Conner H.E.: Some general properties of a class of semilinear hyperbolic systems analogous to the differential-integral equations of gas dynamics.J. Differential Equations 10 (1971), 188–203. Zbl 0219.35061, MR 0289945, 10.1016/0022-0396(71)90046-5; reference:[7] Hillen T.: Existence theory for correlated random walks on bounded domains.Can. Appl. Math. Q. 18 (2010), no. 1, 1–40. Zbl 1201.35127, MR 2722831; reference:[8] Hillen T., Hadeler K.P.: Hyperbolic systems and transport equations in mathematical biology.in Analysis and Numerics for Conservation Laws, G. Warnecke, Springer, Berlin, 2005, pp. 257–279. Zbl 1087.92002, MR 2169931; reference:[9] Horsthemke W.: Spatial instabilities in reaction random walks with direction-independent kinetics.Phys. Rev. E 60 (1999), 2651–2663. MR 1710882, 10.1103/PhysRevE.60.2651; reference:[10] Illner R, Reed M.: Decay to equilibrium for the Carleman model in a box.SIAM J. Appl. Math. 44 (1984), 1067–1075. Zbl 0598.76092, MR 0766188, 10.1137/0144076; reference:[11] Kielhöfer H.: Bifurcation Theory. An Introduction with Applications to PDEs.Appl. Math. Sciences, 156, Springer, New York-Berlin, 2004. MR 2004250; reference:[12] Kmit I., Recke L.: Fredholm alternative for periodic-Dirichlet problems for linear hyperbolic systems.J. Math. Anal. Appl. 335 (2007), 355–370. Zbl 1160.35046, MR 2340326, 10.1016/j.jmaa.2007.01.055; reference:[13] Kmit I., Recke L.: Fredholmness and smooth dependence for linear hyperbolic periodic-Dirichlet problems.J. Differential Equations(to appear). MR 2853567; reference:[14] Lichtner M., Radziunas M., Recke L.: Well-posedness, smooth dependence and center manifold reduction for a semilinear hyperbolic system from laser dynamics.Math. Methods Appl. Sci. 30 (2007), 931–960. MR 2313730, 10.1002/mma.816; reference:[15] Lutscher F., Stevens A.: Emerging patterns in a hyperbolic model for locally interacting cell systems.J. Nonlinear Sci. 12 (2002), no 6, 619–640. Zbl 1026.35071, MR 1938332, 10.1007/s00332-002-0510-4; reference:[16] Platkowski T., Illner R.: Discrete velocity models of the Boltzmann equation: A survey on the mathematical aspects of the theory.SIAM Review 30 (1988), 213–255. Zbl 0668.76087, MR 0941111, 10.1137/1030045; reference:[17] Radziunas M.: Numerical bifurcation analysis of the traveling wave model of multisection semiconductor lasers.Phys. D 213 (2006), 575–613. Zbl 1095.78006, MR 2186586, 10.1016/j.physd.2005.11.003; reference:[18] Radziunas M., Wünsche H.-J.: Dynamics of multisection DFB semiconductor lasers: traveling wave and mode approximation models.in Optoelectronic Devices – Advanced Simulation and Analysis, ed. by J. Piprek, Springer, Berlin, 2005, pp. 121–150.; reference:[19] Slin'ko M.G.: History of the development of mathematical modeling of catalytic processes and reactors.Theoretical Foundations of Chemical Engineering 41 (2007), no. 1, 13–29. 10.1134/S0040579507010022; reference:[20] Zelenyak T.I.: On stationary solutions of mixed problems relating to the study of certain chemical processes.Differ. Equations 2 (1966), 98–102. Zbl 0181.11002; reference:[21] Zelenyak T.I.: The stability of solutions of mixed problems for a particular quasi- linear equation.Differ. Equations 3 (1967), 9–13. Zbl 0214.10002